Membrane transport through stochastically gated channels. Although stochastic gating in channel-facilitated membrane transport has been studied for many decades, there was no theory that explains how the solute flux through the channel depends on the gating rate and solute dynamics in the channel. In 2017 we developed such a theory which showed that significant deviations from the common sense expectations may occur at fast gating when the gating rate becomes comparable with the rate of the solute passage through the channel. This theory was developed assuming that the gate was located at the channel entrance. This year we considered the case of the gate located at the channel exit and showed that the effect of gating on transport is independent of whether the gate is located at the channel entrance or exit. Mechanisms of channel selectivity. We proposed a novel mechanism of channel selectivity which is based on the discovered effects of stochastic gating on channel-facilitated membrane transport. We hypothesized that this mechanism may provide an explanation for the long-known puzzling observation that the outer mitochondrial membrane contains a large number of densely packed voltage-dependent anion channels which are predominantly closed. Collective growth in simple cell networks. We study collective growth in a simple cell network with the goal to rationalize why different cells of the network grow with different rates, the fact observed in the experiment. Diffusion-limited trapping by patchy surfaces. In biological systems, diffusing solutes are typically trapped by active sites on the otherwise reflecting surfaces. We study trapping by patchy surfaces focusing on how the trapping rate depends on the patch size. Analysis of data obtained in single-molecule pulling experiments. When analyzing the data obtained in single-molecule pulling experiments, researches frequently assume that the underlying dynamics of the studied molecule can be described as one-dimensional Markov diffusion with constant diffusivity along a reaction coordinate in the presence of the potential of mean force. In fact, this is not necessarily the case. This dynamics may be non-Markovian. In addition, diffusivity may be position-dependent. We developed a theory which explains how one can (1) discriminate between Markovian and non-Markovian diffusion and (2) determine position-dependent diffusion coefficient from the experimental data.